This invention relates to the field of fluid flow measurement, and in particular to methods and systems for characterizing pulsating flow through vortex flowmeters.
When fluid flows past an obstacle, the obstacle causes a disturbance in the fluid flow. This disturbance is manifested by a vortex generated on one side of the obstacle followed shortly thereafter by another vortex generated on the other side of the obstacle. The two sides of the obstacle continue to alternately generate, or shed, vortices so long as the fluid continues to flow. The frequency at which the two sides of the obstacle shed these vortices is proportional to the velocity of the fluid relative to the obstacle. It is this relationship between the vortex-shedding frequency and the flow velocity that is the basis for the operation of the known vortex flowmeter.
In a vortex flowmeter, an obstacle in the fluid flow, often termed a bluff body, generates the alternating series of vortices. These vortices flow past a transducer, usually a pressure transducer, located at or near the bluff body. Since each vortex is associated with a low pressure zone in the fluid, each time a vortex flows past the pressure transducer, it causes the pressure transducer to generate a pulse having an amplitude proportional to the fluid density and to the square of the fluid velocity. Since the vortices flow with the fluid, the frequency of these pressure pulses, referred to as the xe2x80x9cvortex-shedding frequency,xe2x80x9d is proportional to the fluid velocity. The signal generated by the pressure transducer thus includes a fundamental frequency corresponding to the fluid velocity.
A vortex flowmeter operating in the foregoing manner can provide an accurate measurement of the flow velocity in a fluid-transport system when the fluid flow is either constant or changes slowly compared to the vortex-shedding frequency. Under these circumstances, the vortex-shedding frequency is linearly related to the fluid velocity, as shown in FIG. 1. The slope of the line in FIG. 1, referred to as the xe2x80x9cmeter factor,xe2x80x9d can be empirically obtained in a particular fluid-transport system by calibrating the flowmeter.
A difficulty can arise, however, when the flow varies significantly with time, and in particular when the time-varying flow is a periodic pulsating flow characterized by a pulsation frequency. Such a flow can arise from a variety of sources present in a typical fluid-transport system. These sources include reciprocating pumps, storage tanks having time-varying heads, and resonances in the piping system.
Under these circumstances, most flowmeters are prone to error. In the case of the vortex flowmeter, the pulsating flow and the shedding vortices interact in a manner not fully understood. As a result of this interaction, the vortex-shedding frequency may no longer be linearly related to the fluid velocity, as shown in a representative meter factor curve in FIG. 2. In particular, when the pulsation frequency and the vortex-shedding frequency are nearly harmonically related, the vortex shedding frequency is independent of the fluid velocity, as shown by the discontinuities in FIG. 2.
The source of this difficulty can be understood by consideration of Bernoulli""s equation, which resolves the total pressure applied to a system into two components: a dynamic pressure component, which is proportional to the square of the fluid velocity, and a static pressure component. When the total pressure applied to the system consists of a steady component combined with a pulsatile disturbance, each term in Bernoulli""s equation is likewise the sum of a steady component, representing the system response to the steady component of the total pressure, and a pulsatile component, representing the system response to the pulsatile disturbance in the total pressure. Under these circumstances, the vortex flowmeter measures a velocity that includes a first contribution from the steady component of the dynamic pressure and a second contribution from the pulsatile component of the dynamic pressure. The first contribution corresponds to the desired velocity measurement. The second contribution, which is often assumed to be zero, can introduce an error in the measured vortex flowmeter signal.
The extent to which the pulsatile component of the dynamic pressure contributes to the velocity measured by the vortex flowmeter depends, to a large extent, on the mechanical compliance of the complete fluid-transport system and on the amplitude and frequency of the pulsating flow. As a result, when pulsating flow exists in a fluid-transport system, the system operator""s repertoire of responses, assuming the operator is able to detect the existence of pulsating flow, is limited to: eliminating the source of pulsating flow, heuristically correcting the flowmeter measurement, or accepting the inaccuracy in the flowmeter measurement.
In many cases, the operator is unable to detect the existence of pulsating flow. This is because an operator who observes a particular vortex-shedding frequency has no way of determining whether the observed frequency results from a steady flow at a velocity linearly related to that frequency or whether the vortex-shedding frequency results from pulsatile flow.
In other cases, the operator might ignore a flowmeter signal that suggests a malfunctioning flowmeter when in fact, the flowrneter is correctly tracking the pulsating flow.
When a vortex flows past the pressure transducer in a vortex flowmeter, it causes the transducer to generate a response. As a result, the pressure signal generated by the transducer has a dominant or fundamental frequency corresponding to the rate at which vortices are swept past the pressure transducer. This frequency, which is the vortex-shedding frequency in the absence of any disturbance to the flow, is referred to as the xe2x80x9csteady-state vortex-shedding frequency.xe2x80x9d
When a pulsatile disturbance disturbs the flow, the velocity at which the flow carries the vortices past the transducer varies periodically in response to the disturbance. This variation in flow velocity changes, or modulates, the steady-state vortex-shedding frequency. The resulting pressure signal can thus be considered to be an FM signal having a carrier frequency equal to the steady-state vortex-shedding frequency. A method and system incorporating the principles of the invention uses the spectrum of this FM signal to estimate the pulsatile flow characteristics of the pulsatile disturbance. These pulsatile flow characteristics include the amplitude and pulsation frequency of the pulsatile disturbance.
A method, according to the invention, for determining the pulsation frequency in a fluid flow having a periodically-varying flow velocity includes the steps of generating, and obtaining the measured spectrum of, a flowmeter signal having a carrier frequency modulated by the pulsation frequency. The measured spectrum is then used to estimate the pulsation frequency and amplitude.
In a preferred embodiment, the step of obtaining a measured spectrum includes the step of resolving the measured spectrum into first and second spectral components separated from each other by a gap. The pulsation frequency is then estimated on the basis of the extent of this gap. The relative amplitudes of the spectral components can then be used to estimate the amplitude of the pulsating flow. The estimation of pulsation amplitude and frequency can be accomplished by comparing the measured spectrum to a calibration spectrum corresponding to a known flow condition. The calibration spectrum can be generated empirically or by calculation. In either case, the calibration spectrum can be stored in a database so as to be readily available for comparison with a measured spectrum.
The pulsation amplitude and frequency obtained in the above manner can then be used to correct for any non-linearities in the meter factor and to thereby correct the measurement of flow velocity. This can be accomplished by empirically generating meter-factor calibration curves for a variety of pulsation amplitude and frequency combinations and selecting from this set of calibration curves the meter-factor calibration curve that corresponds to the measured pulsation amplitude and frequency combination.
The flowmeter signal is preferably generated by providing a vortex-generating structure in the fluid flow. Such a structure, which is typically a conventional vortex flowmeter, generates vortices at a vortex-shedding frequency indicative of the flow velocity. These vortices can then be used to generate a flowmeter signal representative of the vortex-shedding frequency.
The invention is not, however, restricted to flowmeters having pressure transducers. The signal processing steps disclosed herein can readily be adapted for use with any flowmeter that generates a flowmeter signal modulated by a pulsatile flow. In particular, the signal processing steps can be applied when the vortices generated by a vortex flowmeter are detected without detecting fluctuations in pressure. For example, there exist vortex flowmeters in which the vortices are detected by illuminating the flow with ultrasonic waves and using a radiation-responsive transducer to detect the phase shift associated with reflections from vortices.
For some combinations of vortex-shedding frequency and pulsation frequency, the resulting signal cannot readily be used to estimate the pulsation amplitude and frequency. It is therefore desirable to predict the occurrence of these combinations. In an optional feature of the invention, the gap between the first and second spectral components is compared to a first selected threshold. If the gap falls below the first selected threshold, the width of the first spectral component is compared to a second selected threshold. If this width falls below the second selected threshold, an alarm signal is generated.
The invention also includes a system for determining, on the basis of a frequency-modulated flowmeter signal, a pulsation amplitude and frequency in a fluid flow having a periodically-varying flow velocity. Such a system includes a spectrum analyzer for obtaining a measured spectrum of the flowmeter signal and a pattern recognition unit coupled to the spectrum analyzer for estimating the pulsation amplitude and frequency on the basis of the measured spectrum.
In a preferred embodiment, the spectrum analyzer includes a spectral resolution process for resolving the measured spectrum into a first spectral component and a second spectral component separated from the first spectral component by a gap representative of the pulsation frequency.
A system embodying the invention optionally includes a vortex-shedding structure, such as a vortex flowmeter, in the fluid flow. Such a structure, when placed in the path of a flowing fluid, generates vortices at a vortex-shedding frequency indicative of the fluid""s flow velocity. A transducer disposed proximately to the vortex-shedding structure detects the vortices and generates a flowmeter signal representative of the vortex-shedding frequency.
Since it is desirable to notify an operator when the pulsation and vortex-shedding frequency are such as to render measurements meaningless, an optional feature of a system embodying the principles of the invention is a thresholding process for determining whether the gap between the first and second components is below a first selected threshold and determining whether the width of the first component is below a second selected threshold. In this case, an alarm signal generator operates in conjunction with the thresholding process to generate an alarm signal when the gap is below the first selected threshold and when the width is below the second selected threshold.